What does Odysseus mean when he
says "this fame has gone abroad to
the sky's rim."?

He describes himself saying - Men hold me formidable for guile in peace and war: this fame has gone abroad to the sky's rim. He describes himself in a way that is very cocky and arrogant.

Explanation:

faith or loyalty when pledged in a solemn agreement or undertaking.

apprenticeships are formal, paid, long-term training programs that provide valuable classroom instruction coupled with on-the-job training for skilled, high-paying jobs.